Subsystem symmetry protected topological order

Abstract

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry groups for such systems exhibit a macroscopic number of generators in the infinite volume limit. We construct a set of exactly solvable models in $2d$ and $3d$ which exhibit such subsystem SPT (SSPT) phases with one dimensional subsystem symmetries. These phases exhibit analogs of phenomena seen in SPTs protected by global symmetries: gapless edge modes, projective realizations of the symmetries at the edge and non-local order parameters. Such SSPT phases are proximate, in theory space, to previously studied phases that break the subsystem symmetries and phases with fracton order which result upon gauging them.

20 pages, 15 figures

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Cited by in corpus (127)

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• Higher order topological superconductors as generators of quantum codes
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
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• Symmetry-protected sign problem and magic in quantum phases of matter
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• Comments on Foliated Gauge Theories and Dualities in 3+1d
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• Compactifying fracton stabilizer models
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• Majorana Quantum Lego, a Route Towards Fracton Matter
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
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• Type-II fractons from coupled spin chains and layers
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• Toy model of boundary states with spurious topological entanglement entropy
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Lattice Clifford fractons and their Chern-Simons-like theory
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• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Duality viewpoint of criticality
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• Classification and construction of interacting fractonic higher-order topological phases
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
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• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
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• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
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• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
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• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Many-body quantum catalysts for transforming between phases of matter
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
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• Fractonic superfluids. III. Hybridizing higher moments
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• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass
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